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E470: Chapter 2

E470: Chapter 2. OLS = Ordinary Least Squares. -ordinary… -least squares: minimize sum of squared residuals. OLS = Ordinary Least Squares. -ordinary -least squares: minimize sum of squared residuals -wildly inaccurate positives and negatives (not squared) would merely offset each other

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E470: Chapter 2

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  1. E470: Chapter 2

  2. OLS = Ordinary Least Squares -ordinary… -least squares: minimize sum of squared residuals

  3. OLS = Ordinary Least Squares -ordinary -least squares: minimize sum of squared residuals -wildly inaccurate positives and negatives (not squared) would merely offset each other -makes large residuals rel. painful and thus, desirable to deal with

  4. How well does the model fit?? defining TSS, ESS, RSS • TSS = (Y - Y bar)2; Y bar is a constant-- the "naive estimator" • TSS is a given; goal: explain as much as possible

  5. How well does the model fit?? defining TSS, ESS, RSS • TSS = (Y - Y bar)2; Y bar is a constant-- the "naive estimator" • TSS is a given; goal: explain as much as possible • ESS (Explained/Estimated) = (Y hat - Y bar)2; the change (almost always an improvement) from using a better estimator

  6. How well does the model fit?? defining TSS, ESS, RSS • TSS = (Y - Y bar)2; Y bar is a constant-- the "naive estimator" • TSS is a given; goal: explain as much as possible • ESS (Explained/Estimated) = (Y hat - Y bar)2; the change (almost always an improvement) from using a better estimator • RSS = (Y - Y hat)2; how much the estimated value differs from the observed value

  7. How well does the model fit?? defining TSS, ESS, RSS • TSS = (Y - Y bar)2; Y bar is a constant-- the "naive estimator" • TSS is a given; goal: explain as much as possible • ESS (Explained/Estimated) = (Y hat - Y bar)2; the change (almost always an improvement) from using a better estimator • RSS = (Y - Y hat)2; how much the estimated value differs from the observed value --> in sum, a primary goal: find Y hat so as to improve over Y bar; max ESS, limit RSS

  8. Interpreting Variable Coefficients and other stats • implicitly, ceteris paribus

  9. Interpreting Variable Coefficients and other stats • implicitly, ceteris paribus • estimated vs. expected signs -as a problem or as time to change/theory

  10. Interpreting Variable Coefficients and other stats • implicitly, ceteris paribus • estimated vs. expected signs -as a problem or as time to change/theory • tightness of model/variable fit -R2 • measures goodness of fit for the model (vs. "goodness of fit" for variable coefficients; more later) • not the end-all; primary, but not only goal

  11. Interpreting Variable Coefficients and other stats • implicitly, ceteris paribus • estimated vs. expected signs -as a problem or as time to change/theory • tightness of model/variable fit -R2 • measures goodness of fit for the model (vs. "goodness of fit" for variable coefficients; more later) • not the end-all; primary, but not only goal • CS vs. TS; CS lower since it's easier to miss variables • R2 near one is usually trouble (more later)

  12. Interpreting Variable Coefficients and other stats • implicitly, ceteris paribus • estimated vs. expected signs -as a problem or as time to change/theory • tightness of model/variable fit -R2 • measures goodness of fit for the model (vs. "goodness of fit" for variable coefficients; more later) • not the end-all; primary, but not only goal • CS vs. TS; CS lower since it's easier to miss variables • R2 near one is usually trouble (more later) -”adjusted” R2 • reducing d.f.; add variables adds explanatory power? (F-test )

  13. Interpreting Variable Coefficients and other stats • implicitly, ceteris paribus • estimated vs. expected signs -as a problem or as time to change/theory • tightness of model/variable fit -R2 • measures goodness of fit for the model (vs. "goodness of fit" for variable coefficients; more later) • not the end-all; primary, but not only goal • CS vs. TS; CS lower since it's easier to miss variables • R2 near one is usually trouble (more later) -”adjusted” R2 • reducing d.f.; add variables adds explanatory power? (See: F-test later) • correlation coefficients (+1, -1, 0)

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